Simplify the following expression: $ q = \dfrac{-7}{10} - \dfrac{7y + 6}{8y} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8y}{8y}$ $ \dfrac{-7}{10} \times \dfrac{8y}{8y} = \dfrac{-56y}{80y} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{7y + 6}{8y} \times \dfrac{10}{10} = \dfrac{70y + 60}{80y} $ Therefore $ q = \dfrac{-56y}{80y} - \dfrac{70y + 60}{80y} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-56y - (70y + 60) }{80y} $ Distribute the negative sign: $q = \dfrac{-56y - 70y - 60}{80y}$ $q = \dfrac{-126y - 60}{80y}$ Simplify the expression by dividing the numerator and denominator by 2: $q = \dfrac{-63y - 30}{40y}$